Algebraic reconstructions
X-ray medical imaging. 3D image processing

For many years now, major efforts have been focused on developing algebraic reconstruction techniques as alternatives to FBP-type analytical techniques, with the main aim of significantly reducing the dose to the patient, at the cost of much heavier calculations, since these methods are iterative. They may seem more intuitive than analytical methods, but their apparent simplicity masks the great complexity of the calculations, the very large number of possible approaches (an indication that experience has not made it possible to sort them out), and although they have been used for decades in nuclear medicine (PET and more recently SPECT), they are still the subject of research at the cutting edge of mathematics. In addition to providing finer noise management than analytical methods, they offer a better description of the "patient – radiography system" ensemble through a "projection matrix"...